(197c) Simulation of liquid phase maldistribution during the extrusion of highly filled particulate pastes

Particulate pastes are widely used to manufacture products such as foods, agrochemicals, pharmaceuticals, ceramics and solder pastes using common processing techniques such as ram extrusion and injection moulding. These materials are soft solids and feature a high volume fraction of particulate solids in a liquid binder. Their rheology is therefore strongly influenced by interparticle contacts, i.e. rather than collisions, and exhibits complex yield stress behaviour and wall slip. Furthermore, several types of paste- specific flaw may develop during processing, as discussed by Benbow & Bridgwater (1993, p. 21).

One such flaw is liquid phase maldistribution (or migration), henceforth abbreviated to LPM. When stresses are applied to a paste during ram extrusion, a direct consequence of the multi-phase nature of pastes is that the applied stress is split between the load-bearing particulate network (the solids skeleton) and the liquid present in the gaps (pores) between the particles. These pores form an interconnected network that is permeable to the liquid. If the applied stress varies spatially across the paste, pore liquid pressure gradients develop within the pore network and drive flow of the liquid relative to the solids skeleton. LPM will thus result in an inhomogeneous distribution of liquid. Since the rheological properties of the paste are strongly dependent by liquid content, flow patterns are modified and dead zones may result. In extreme cases of LPM, flow will cease completely, causing damage to the extruder and loss of production.

Detailed and reliable simulation of the paste extrusion process is required to improve design of dies but can also be used to study flaws such as LPM. The aim of the latter simulations is to link the severity of LPM to the operating conditions and the composition (or formulation) of the paste: the onset of LPM occurs when the relative velocity of the local pore liquid is large compared to the absolute velocity of the solids, so that the liquid has time to redistribute while the paste passes through a high stress region, i.e. the die entry zone in a ram extruder. The relative velocity of the liquid phase to the solids skeleton is a function of the (local) pore liquid pressure gradient and the permeability of the solids skeleton. The latter parameter is determined by the properties of the particles (absolute particle size, size distribution, shape, roughness and deformability), the skeleton (solids volume fraction), liquid (rheology, liquid volume and air volume fractions for unsaturated pastes), and chemical interactions between the solids and the liquid.

Models for paste flow incorporating LPM do exist for ram extrusion, e.g. Rough et al. (2002) and squeeze flow, e.g. Poitou & Racineux (2001), Sherwood (2002), Kolenda et al. (2003) and Roussel et al. (2003). However these models are currently either one-dimensional, geometry-specific or do not incorporate some of the more complex features of pastes such as dilatancy of the solids network when it is subject to shear. Two-phase modelling approaches which do incorporate these effects are well established in the field of soil mechanics and the challenge is to apply these models to simulate paste extrusion processes, where the strains are much larger than normally arise in soil problems.

The work reported here represents the initial application of a soil mechanics constitutive law, namely modified Cam-Clay, to simulating the ram extrusion of saturated pastes through a coaxial cylindrical barrel and die land. The liquid is modelled as Newtonian and incompressible, and Darcy's law is used to represent the interactions between the two phases. This is implemented in a two-dimensional axisymmetric finite element method (FEM) simulation. A series of simulations have been performed in order to investigate the effect of selected formulation parameters on paste performance during extrusion.

References

Benbow, J.J. & Bridgwater, J. (1993) Paste Flow and Extrusion, Clarendon Press. Kolenda, F., Retana, P., Racineux, G. & Poitou, A. (2003) Identification of Rheological Parameters by the Squeezing Test, Powder Technology, 130, p. 56. Poitou, A. & Racineux, G. (2001) A Squeezing Experiment Showing Binder Migration in Concentrated Suspensions, Journal of Rheology, 45, p. 609. Rough, S.L., Wilson, D.I. & Bridgwater, J. (2002) A Model Describing Liquid Phase Migration within an Extruding Microcrystalline Cellulose Paste, Chemical Engineering Research and Design, 80, p. 701. Roussel, N., Lanos, C. & Melinge, Y. (2003) Induced Heterogeneity in Saturated Flowing Granular Media, Powder Technology, 138, p. 68. Sherwood, J.D. (2002) Liquid-Solid Relative Motion During Squeeze Flow of Pastes, Journal of Non-Newtonian Fluid Mechanics, 104, p. 1.